The number of real solutions of the equation x² − 3|x| + 2 = 0 is:

Correct option is A

Given:

Equation: x² − 3|x| + 2 = 0

Concept used:
Let |x| = t, where t ≥ 0.
Then the equation becomes: t² − 3t + 2 = 0

Solution:

t² − 3t + 2 = 0
=> (t − 1)(t − 2) = 0
=> t = 1 or t = 2

Now, since |x| = t,
If |x| = 1 => x = ±1
If |x| = 2 => x = ±2

So, x = 1, −1, 2, −2

Total real solutions = 4

Correct answer is (a) 4.